Dynamics for the Cl+C2H6-+HCl+C2H5 reaction examined through state-specific angular distributions

Article abstract of DOI:10.1063/1.472581

Photolysis of Cl₂ initiates the title reaction at a sharply defined collision energy of 0.24±0.03 eV. Nascent product rotational state distributions for HCl (v=0) are determined using resonance enhanced multiphoton ionization (REMPI), center-of-mass scattering distributions are measured by the core-extraction technique, and the average internal energy of the C₂H₅ product is deduced from the dependence of the core-extracted signal on the photolysis polarization. The HCl product has little rotational excitation, but the scattering distribution is nearly isotropic. Although seemingly contradictory, both of these features can be accounted for by using the simple line-of-centers model presented to explain earlier results for the Cl+CH₄ reaction. In contrast to the Cl+CH₄ reaction, the data suggest that the Cl+C₂H₆ reaction proceeds through a loosely constrained transition-state geometry. The reactions of atomic chlorine With ethane, C₂H₆, and perdeuteroethane, C₂D₆, yield virtually identical results. These findings, along with the low energy deposited by the reaction into the ethyl product (200±120 cm^-1), demonstrate that the alkyl fragment acts largely as a spectator in this hydrogen abstraction reaction.

Full text of DOI:10.1063/1.472581

Dynamics for the Cl+C2H6→HCl+C2H5 reaction examined through statespecific
angular distributions
S. Alex Kandel, T. Peter Rakitzis, Topaz LevOn, and Richard N. Zare
Citation: The Journal of Chemical Physics 105, 7550 (1996); doi: 10.1063/1.472581
View online: http://dx.doi.org/10.1063/1.472581
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Dynamics for the Cl؉C2H6˜HCl؉C2H5 reaction examined through
state-specific angular distributions
S. Alex Kandel, T. Peter Rakitzis, Topaz Lev-On, and Richard N. Zare
Department of Chemistry, Stanford University, Stanford, California 94305
͑Received 26 April 1996; accepted 23 July 1996͒
Photolysis of Cl2 initiates the title reaction at a sharply defined collision energy of 0.24Ϯ0.03 eV.
Nascent product rotational state distributions for HCl ͑ ϭ0͒ are determined using resonance
v
enhanced multiphoton ionization ͑REMPI͒, center-of-mass scattering distributions are measured by
the core-extraction technique, and the average internal energy of the C2H5 product is deduced from
the dependence of the core-extracted signal on the photolysis polarization. The HCl product has
little rotational excitation, but the scattering distribution is nearly isotropic. Although seemingly
contradictory, both of these features can be accounted for by using the simple line-of-centers model
presented to explain earlier results for the ClϩCH4 reaction. In contrast to the ClϩCH4 reaction, the
data suggest that the ClϩC2H6 reaction proceeds through a loosely constrained transition-state
geometry. The reactions of atomic chlorine with ethane, C2H6, and perdeuteroethane, C2D6, yield
virtually identical results. These findings, along with the low energy deposited by the reaction into
the ethyl product ͑200Ϯ120 cmϪ1͒, demonstrate that the alkyl fragment acts largely as a spectator
in this hydrogen abstraction reaction.
© 1996 American Institute of Physics.
͓S0021-9606͑96͒00341-8͔
I. INTRODUCTION
properties of the products need to be measured. Nonetheless,
extreme diligence is required for detailed studies of such
systems; complete product state and scattering information
has been achieved in only a few cases, for example FϩH2
͑Refs. 2 and 3͒ and HϩH2.4,5 The large number of degrees of
freedom in an atom/polyatom reaction magnifies the diffi-
culty of the problem and usually results in a reduced degree
of information obtained compared with these benchmark
atom/diatom reactions.
After providing an experimental overview, we present
HCl product state distributions and state-resolved angular
distributions. Spatial anisotropy measurements are then dis-
cussed as a means of determining the average energy depos-
ited into the unobserved C2H5 product. We briefly present
data concerning how the scattering changes with product ro-
tation and compare the ClϩC2H6 reaction with its fully deu-
terated analog. A simple, intuitive, and self-consistent model
is presented to explain these results. Comparisons with other
reactions of hydrocarbons with atomic chlorine are made,
including an extended discussion of the closely related
ClϩCH4 reaction.
A microscopic understanding of bimolecular chemical
reactions requires investigation of the conditions under
which the two reagents come together, the forces that medi-
ate reagent interaction, and the nature of the products
formed. The rigor pursued in the description of a reaction
varies greatly. A few reactive systems have been explained
in great detail through the use of theoretical calculations on
ab initio potential energy surfaces. In contrast, many single
or related groups of reactions are understood through quasi-
classical, classical, or even nonquantitative intuitive models.
The present investigation aims to provide data necessary for
both rigorous and intuitive descriptions. Our experimental
approach is to measure the state-specific angular scattering
distributions for a bimolecular reaction product. The result-
ing picture of product motions leads immediately to a physi-
cal understanding of the reactive process, and the quantita-
tive data allows direct comparison with the results of
theoretical studies.
This paper presents correlated state and scattering mea-
surements for the gas-phase reaction of ground-state chlorine
atoms with ethane molecules to produce hydrogen chloride
and ethyl radicals
II. EXPERIMENT
2
Cl P ͒ϩC2H6→HClϩC2H5.
͑
3/2
The experimental apparatus and techniques have been
described elsewhere, and a brief overview is detailed here.
Molecular chlorine ͑Matheson Gases, 99.999%͒, ethane
͑Matheson Gases, 99.99%͒, and helium carrier gas ͑Liquid
Carbonic, 99.995%͒ are premixed in a Teflon-lined tank. If
shielded from light, this mixture does not produce significant
amounts of HCl even when allowed to stand for days. The
mixture is then fed through Teflon coils maintained at
Ϫ78.5 °C ͑dry ice/ethanol mixture͒ to remove impurities
produced by metal corrosion or reaction with pump oils or
Kinetic studies have established this reaction to be slightly
exothermic by 2.65 kcal/mol ͑928 cmϪ1, 0.115 eV͒, with a
rate constant of 5.9ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1 at 298 K.1
No theoretical or experimental investigations have detailed
the microscopic dynamics of this reactive system. Indeed,
few reactions involving polyatomics have been studied from
a dynamical standpoint. In an atom/diatom reaction ͑the tra-
ditional domain of reaction dynamics͒, a small number of
experimental variables need to be constrained and a few
7550
J. Chem. Phys. 105 (17), 1 November 1996
0021-9606/96/105(17)/7550/10/$10.00
© 1996 American Institute of Physics
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Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
7551
greases; the gas mixture is then immediately coexpanded
through a pulsed nozzle ͑General Valve 9-Series, 0.6 mm
orifice͒ at 380 Torr backing pressure.
speed distribution. This method can be used to obtained the
entire three-dimensional velocity distribution through the use
of the core extractor, a mask that is placed in front of the
detector and rejects products scattered off the detection axis.
The lab-frame velocity of the reaction product is the vec-
tor sum of the center-of-mass velocity and the center-of-
mass-frame product velocity. The former is determined by
the coexpansion of reagents and the single-channel photoly-
sis, as detailed earlier; the latter is determined by the ener-
getics of the reaction, the selection of the product HCl inter-
nal energy state to be measured, and an assumption about the
internal energy deposited into the unobserved C2H5 product.
The determination of these two vectors, along with the mea-
surement of the third, uniquely defines all angles of the tri-
angle formed, in particular, the center-of-mass scattering
angle. Thus, the measured lab-frame speed distribution is
transformed into the center-of-mass distribution of scattering
angles, which yields the state-resolved differential cross sec-
tion for the reaction. This method for measurement of the
differential cross section, which we call the photoloc
method, has been used successfully by several investigators
for an increasing number of reactive systems.4,13,17–24
The reaction is initiated by photolysis of Cl2 at 355 nm
using the third harmonic of a Nd3ϩ:YAG laser. At this fre-
quency, more than 98% of the chlorine atoms are produced
2
in their ground state ͑Cl P3/2͒;6 consequently, almost all are
moving at a single speed of 1680 m/s. The molecular chlo-
rine precursor and the ethane molecules are assumed by vir-
tue of translational cooling in a jet expansion to have very
little motion with respect to each other. Therefore, the pho-
tolysis defines the relative motion between the chlorine atom
and ethane molecule reagents, which produces a narrow dis-
tribution of center-of-mass collision energies for the reaction
at 1900 cmϪ1 with a 420 cmϪ1 Gaussian spread ͑FWHM͒.
This spread, which results from residual thermal motion of
the jet-cooled reagents, is calculated using a 15 K transla-
tional temperature.6 This value is a conservative estimate
based on the measured 15 K rotational temperature of con-
taminant HCl in the expansion.
HCl products are allowed to build for 50–100 ns before
they are detected with rovibrational state specificity via
1
3
͑2ϩ1͒ REMPI through the F ⌬2 state7–11 or the f ⌬2
state.7–9 Frequency-doubled light at 240–243 nm from a
Nd3ϩ:YAG-pumped dye-laser system ͑Spectra-Physics DCR
2A and PDL-3; Exciton, LD489 dye͒ drives the REMPI pro-
cess at the focus of a 50 cm lens. The photolysis laser is
more gently focused to a 1 mm beam diameter. Neither chlo-
rine atoms nor reactive products are moving rapidly enough
to traverse the photolysis beam radius on the time scales
allowed for reaction; therefore, chlorine atom densities are
constant in time, and reactive product concentrations build
linearly after photoinitiation of the reaction. A slight correc-
tion accounting for the Gaussian profile of the photolysis
beam is applied to speed-sensitive measurements of the
product. A linear time-to-flight ͑TOF͒ mass spectrometer en-
ables the separation of resonantly produced H35Clϩ and
H37Clϩ from a variety of other background ions. Integration
of the total H35Clϩ signal as the REMPI wavelength is
scanned over the HCl excitation spectrum results in the prod-
uct state distribution from the reaction, after correction by
empirical linestrength factors.11–14
Measurement of the HCl speed distribution is accom-
plished using the method of core extraction, which has been
described extensively by Simpson et al.;15 a thumbnail
sketch is provided here. HCl products are formed with some
nascent distribution of velocities, determined by the initial
speed of the reagents and the scattering behavior of the sys-
tem, as described below. The photoionization process im-
parts virtually no velocity to the created ions, so that the
initial speeds of the HClϩ to be detected mirror those of the
neutral precursors. The ion velocities create a spread in the
ion packet as the packet travels in the mass spectrometer
toward the detector. Faster velocities spread more, and
slower ones less, as in a Doppler profile. The mass spectrom-
eter is of Wiley–McLaren design16 and is operated under
space-focusing and velocity-sensitive conditions; therefore,
this ion profile can be inverted directly to the original HCl
Calculation of the differential cross section is predicated
on the assumption of the internal energy of the unobserved
product. Although this assumption is usually correct for
atom/diatom systems, polyatomic reagents lead to poly-
atomic products, and one goal of the experiment is to under-
stand the dynamical participation of both products. Making
assumptions about the behavior of the unobserved product is
therefore unsatisfying; furthermore, the increased number of
degrees of freedom of a polyatomic product make these as-
sumptions likely to be faulty. Therefore, a further measure-
ment is performed to determine the angle between the center-
of-mass velocity and the product lab-frame velocity. This
angle allows a second use of the law of cosines to determine
the center-of-mass product velocity without the need for as-
sumptions. Unfortunately, this angle cannot be measured ex-
actly in the current experiment. An averaged quantity related
to this angle is obtained, however, in the measurement of the
spatial anisotropy of the HCl product. This measurement is
carried out by changing the linear polarization direction of
the photolysis beam on alternate photolysis laser shots so
that the electric vector of the photolysis light lies either par-
allel or perpendicular to the time-of-flight axis. The polariza-
tion flipping is effected by synchronization to the stress cycle
of a photoelastic modulator ͑Hinds International, PEM-80͒,
and the resulting polarizations have a transmittance ratio of
at least 16:1 through a linear polarizer.
III. RESULTS
A. Rotational state distributions
HCl REMPI spectra were recorded on R- and S-branch
transitions of the F–X͑0,0͒ band and Q-branch transitions of
the f –X͑0,0͒ band, with total m/zϭ36 ͑H35Clϩ͒ ion signal
collected and integrated. The signals in these spectra were
converted to populations using previously published correc-
1
tion factors11–13 for the F ⌬2 state and correction factors for
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7552
Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
FIG. 2. The energetics of the reaction of atomic chlorine with ethane. The
collisional energy spread is calculated following van der Zande et al.6 as-
suming a 15 K beam translational temperature.
FIG. 1. Plot of the state distribution for the HCl ( ϭ0,J) product from the
v
reaction of atomic chlorine with ground-state ethane. Error bars represent 1␴
statistical deviations. Relative populations are determined from REMPI
spectra as described in the text.
threshold, other sources of formation cannot be discounted,
especially reaction of ethane with Cl͑2P1/2͒ present as 2% of
3
the f ⌬2 state obtained from thermal HCl spectra.14 The
our atomic chlorine reagent. Therefore, results for HCl͑ ϭ1͒
v
HCl( ϭ0,J) product rotational state distribution from the
v
cannot be made quantitative at this time.
ClϩC2H6 reaction is presented in Fig. 1, which shows a cold
rotational distribution with 48Ϯ3 cmϪ1 average energy in
rotation. Levels of contaminant HCl present in our gas mix-
ture before reaction were small compared with signal mag-
nitudes; this contamination was eliminated from the col-
lected signal through the use of photolysis on/off subtraction.
The photolysis laser was operated at half the repetition rate
of the probe, which allowed subtraction of signals on an
every-other-shot basis. Because most backgrounds, including
contaminant HCl, did not rely on the presence of the pho-
tolysis laser, they were thus eliminated by this subtraction
procedure. Because the reactive signal depends on the pho-
tolysis for the production of the chlorine atom reagent, the
result of the on/off subtraction is to separate the reactive
signal from possible background interference. The photolysis
laser alone caused no ionization.
The time dependence of product formation was mea-
sured to check the nascency of the state distribution. We
verified that for several rotational states across the distribu-
tion, the state distribution did not vary with the time delay
between reaction initiation and product probe on the times-
cales allowed for reactive product buildup. Additionally,
products were seen to build linearly with this delay, as is
expected at short delays during which reagent chlorine con-
centration does not change. The intercept of this linear
growth could be extrapolated to zero product at laser over-
lap. Thus, we have seen no evidence of either HCl product
relaxation or HCl formation from photodissociation of pos-
sible Cl2/C2H6 clusters.
B. Speed distributions and angular scattering
In the measurement of ion-arrival-time profiles for the
determination of speed distributions and thus differential
cross sections, removal of background was accomplished us-
ing time-jump subtraction. In this subtraction procedure, the
photolysis/probe time delay is alternated every 20 laser shots
between two values: A short time delay for which back-
ground contributions and very little reactive signal are
present, and a longer time delay with the same background
contributions and more signal allowed to build up. This dif-
ferencing procedure results only in signals that change with
delay between photolysis and probe laser pulses, which
eliminates essentially all background interference from the
measurement of reactive signal. This more rigorous subtrac-
tion procedure is necessary for velocity-sensitive detection,
in which quickly moving H35Clϩ overlaps at the detector
with both 35Clϩ and 37Clϩ backgrounds. Additionally, for
small signals ͓HCl͑ ϭ0, Jϭ6͒ and HCl͑ ϭ0, Jϭ8͒ prod-
v
v
ucts͔ photolysis and probe-induced C2Hϩn background contri-
butions necessitated a linear baseline correction for arrival
profiles.
The three-dimensional velocity distribution of the HCl
product is determined using core-extracted ion-arrival-time
profiles. Two distinct profiles were recorded for each product
state: One with the photolysis laser polarization perpendicu-
lar to the flight axis, referred to as Iperp ; the other with the
polarization parallel, referred to as Ipar . These profiles were
recorded concurrently, with the polarization alternating every
other laser shot. The Cl2 photolysis, which has a pure sin2 ␪
distribution ͑␤ϭϪ1͒ for Cl͑2P3/2͒ at this frequency,25 is the
only source of anisotropy in the experiment. Therefore, mea-
surements at any two polarizations contain all of the infor-
mation describing the three-dimensional velocity distribution
Vibrationally excited HCl͑ ϭ1͒ was also observed as a
v
reaction product. This product state is not strictly energeti-
cally allowed, as shown in Fig. 2, but it is permissible within
our spread of collision energies. We measured the ratio of
HCl͑ ϭ0͒:HCl͑ ϭ1͒ populations to be 300:1. Given the
v
v
amount of population and the nearness of this channel to
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Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
7553
FIG. 4. Differential cross section for the reactive product HCl ͑ ϭ0, Jϭ1͒,
v
calculated from the measured speed distribution shown in Fig. 3. The cal-
culation requires an assumption of the C2H5 internal energy. For this analy-
sis, the ethyl fragment is assumed to take negligible energy into internal
modes; this assumption is discussed extensively in the text.
these basis functions were chosen to be equally spaced in
speed, which reflects the experimental resolution. The result-
FIG. 3. ͑a͒ Core-extracted ion-arrival profile for HCl ͑ ϭ0, Jϭ1͒, along
v
ing speed distribution for HCl͑ ϭ0, Jϭ1͒ product is shown
v
with the calculated best fit function. Spatial anisotropy has been removed by
forming a composite profile from the isotropic sum, IisoϭIparϩ2Iperp of pro-
files measured with the photolysis polarization parallel and perpendicular to
in Fig. 3͑b͒; the 1␴ error bar for each speed is determined
from statistical variation in replicate measurements.
the TOF axis. ͑b͒ Speed distribution of HCl ͑ ϭ0, Jϭ1͒ resulting from a
v
The reaction is able energetically to populate speeds
ranging from 0 to 1815 m/s. The speed distribution shows a
small amount of slowly moving product, increasing steadily
to a maximum near the fastest speeds allowable. For the
moment we make the assumption, supported later, that the
C2H5 fragment takes none of the energy available to the re-
action into internal excitation. Using this assumption, we can
easily convert the product speed to the center-of-mass scat-
tering angle, as explained earlier. Figure 4 shows a plot of
the differential cross section against the cosine of the scat-
tering angle. The uneven spacing of the points in this graph
along the cos ␪ axis makes the nonlinearity of this conver-
sion evident and emphasizes that while the experimental
resolution is constant in speed, it varies with respect to cos ␪.
The associated volume element for this conversion is what
transforms a large preference for the formation of faster over
slower products into nearly equal amounts of forward-
scattered ͑cos ␪ϭ1͒ and backward-scattered ͑cos ␪ϭϪ1͒
products.
Note that large product rotational alignment effects, if
present, would complicate this analysis and must be evalu-
ated along with the speed distribution.26–28 Small HCl
velocity/rotation vector correlations have been observed in
the ClϩCH4 system.29 These correlations are determined ex-
perimentally through changes in core-extracted time profiles
dependent on the REMPI probe laser polarization. We have
performed probe polarization-flipping experiments on sev-
eral HCl product states for ClϩC2H6 and have observed
measurable but very small changes in the time profiles
͑Ϸ5%͒. These changes are small enough to be ignored for
purposes of determining speed and anisotropy distributions.
maximum-entropy analysis that fits the arrival profile to a combination of
instrumental basis functions. Error bars represent 1␴ statistical deviations of
replicate measurements.
of the product. Analysis of these time profiles is accom-
plished in two steps through the formation of two composite
profiles. The first composite profile Iiso is formed as the sum
I
parϩ2Iperp . This sum removes all spatial anisotropy from
the data and is thus analyzed straightforwardly to yield the
speed distribution. The second composite profile Ianiso con-
tains the anisotropic component of the spatial distribution
and is analyzed in Sec. III C to yield the speed dependence
of the second Legendre moment, ␤prod
Figure 3͑a͒ shows the core-extracted composite time
profile Iiso for HCl͑ ϭ0, Jϭ1͒ product from the ClϩC H
.
v
2
6
reaction, recorded with a 62 V/cm extraction field. The data
were analyzed in a fashion similar to that described
previously.15 A set of basis functions, each describing the
instrumental response to a monoenergetic speed distribution,
was constructed and calibrated to Cl atoms at known speeds.
Owing to the slow product speeds possible for this reaction,
further calibration was performed using Cl͑2P1/2͒ from 481
to 491 nm photolysis of Cl ͑ ϭ1͒;25 this photolysis pro-
v
2
duced monoenergetic speed distributions tunable between
130 and 400 m/s. Basis functions were constructed for pho-
tolysis polarizations parallel and perpendicular to the TOF
axis. Composite isotropic and anisotropic basis functions,
analogous to the isotropic and anisotropic profiles, were then
used to fit the data. Profiles were fit to a linear combination
of basis functions using a maximum-entropy analysis;15,18
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7554
Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
FIG. 5. Core-extracted ion-arrival profile for HCl ͑ ϭ0, Jϭ1͒. This profile
v
is a composite that contains product spatial anisotropy information; the pro-
file is generated as twice the anisotropic difference of experimental profiles
measured with the photolysis polarization parallel and perpendicular to the
TOF axis, Ianisoϭ2͑IparϪIperp͒. The solid line shows the fit to the data as a
sum of instrumental basis functions obtained through a least-squares fitting
algorithm.
C. Speed-dependent spatial anisotropy
FIG. 6. Three representative basis functions that predict instrumental re-
sponse for a composite anisotropic profile for single-speed products at 91,
912, and 1733 m/s, all with spatial anisotropy ␤ϭϪ1. The basis functions
showing instrumental response to isotropic profiles for each speed are
shown as dotted lines to demonstrate sensitivity to anisotropy.
The
composite
core-extracted
time
profile
I
anisoϭ2͑IparϪIperp͒ for HCl͑ ϭ0, Jϭ1͒ is shown in Fig. 5.
v
This profile is once again fit to a linear combination of basis
functions. These basis functions are anisotropic composites
of parallel and perpendicular bases and mimic the instrumen-
tal sensitivity to product spatial anisotropy. Three represen-
tative functions are shown in Fig. 6, along with correspond-
ing isotropic basis functions. The sensitivity to spatial
anisotropy is strongest at high speeds, as evidenced by the
large, sharply peaked form of the fastest anisotropic basis
function. The core extractor causes this behavior at these
product speeds by preferentially selecting products with little
velocity transverse to the detection axis. The slower product
speeds are less effectively discriminated, and the sensitivity
to anisotropy is correspondingly decreased. Fitting to the
profile Ianiso was accomplished using a Levenburg–Marquart
nonlinear least squares algorithm,30 which determined the
first two or three Legendre moments of the speed-dependent
spatial anisotropy. Alternate analyses yield nearly identical
results. Figure 7 shows the result of the least squares Leg-
endre fit, along with replicate measurement 1␴ error bars.
This plot of spatial anisotropy describes the product spatial
distribution as a function of lab-frame speed,
relative reagent masses. If the center-of-mass scattering
angle ␪
were known, the product speed in the center of
com
mass frame uHCl could be calculated from
2
2
1/2
uHCl
ϭ
Ϫ
1Ϫcos2 ␪
͒
͔
com
͓vHCl vcom
͑
Ϫ
cos ␪
,
͑2͒
vcom
com
so that ␪ is given by
lab
d␴
͑vHCl ͑ ͔
͒P2 cos ␪ ͒ , ͑1͒
phot
I
HCl ,␪ ͒ϭ
1ϩ␤
͑v
͓
phot
d
vHCl
in terms of the angle ␪phot , which is defined relative to the
polarization vector of the photolysis laser. The quantity
␤͑
vHCl
͒ is plotted against
in the figure.
vHCl
Consider HCl products in a measured internal state
FIG. 7. HCl ͑ ϭ0, Jϭ1͒ product spatial anisotropy as a function of speed,
␤( ), resulting from analysis of the anisotropic time profile shown in Fig. 5.
v
v
( ,J) with a measured lab-frame speed HCl ; the center-of-
v
v
mass speed
is determined by the reagent speed and
Error bars represent 1␴ statistical deviations of replicate measurements.
vcom
J. Chem. Phys., Vol. 105, No. 17, 1 November 1996
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Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
7555
FIG. 8. ͑a͒ HCl product spatial anisotropy as a function of speed, as in Fig.
7, with added contours that indicate the calculated relationship between ␤
and for varying degrees of C2H5 internal excitation. The outermost curve
v
shows the predicted form for ␤( ) assuming no C H internal excitation;
v
2
5
inner contours are spaced by 500 cmϪ1 in ethyl excitation. ͑b͒ C2H5 internal
energy excitation plotted as a function of HCl velocity. This plot results
from a transformation of the data shown in Fig. 8͑a͒, as detailed in the text.
FIG. 9. Ion arrival profiles and differential cross sections for HCl ͑ ϭ0͒
v
products: Jϭ1, Jϭ3, Jϭ6, and Jϭ8. The profiles are narrower at higher
rotational levels, which indicates slower product velocities and thus a trend
toward back-scattering in the differential cross section.
2
2
ϩ
comϪu2HCl
vHCl
v
cos ␪labϭ
,
͑3͒
2
vHClvcom
where ␪ is the angle between the lab-frame velocity,
of the HCl product and the center-of-mass velocity,
,
,
product speed. In Fig. 8͑b͒, the inverted parabola is drawn to
show the amount of available energy not appearing in prod-
uct translation. Averaging the internal energy for each speed,
weighted by the measured speed distribution, yields a C2H5
internal energy of 200Ϯ120 cmϪ1. This low degree of inter-
nal excitation justifies the assumption made earlier in trans-
forming the speed distribution into the differential cross sec-
tion. Similar measurements of product internal excitation
through spatial anisotropy measurements have been per-
formed for several other systems.5,13,21 The treatment pre-
sented here allows for direct inversion of the data to produce
vHCl
vcom
lab
which lies along the velocity of the Cl reagent. Thus, HCl
product at a given speed uHCl and center-of-mass scattering
angle ␪com appears in the laboratory with angle ␪lab in a cone
about every Cl reagent velocity. This analysis leads to an
expression for the spatial anisotropy of the product
␤
͒ϭ␤ClP2 cos ␪ ͒.
͑4͒
͑vHCl
HCl
͑
lab
Thus, we see that knowledge of the center-of-mass scattering
angle allows direct calculation of the lab-frame anisotropy
and the center-of-mass velocity. Because in most cases mul-
tiple scattering angles are possible for a given value of the
␤( ), as contrasted with methods that assume internal exci-
v
tation and then forward convolute to fit anisotropy data.
measured speed HCl , ␤HCl is an inherently averaged quantity
v
that cannot be inverted to yield the scattering angle or center-
of-mass velocity without further knowledge of the distribu-
D. Speed distribution dependence on product
rotation
tion of angles averaged. The measurement of ␤( ) through
v
the use of anisotropic core-extracted time profiles nonethe-
less provides dynamical insight into the behavior of the C2H5
product.
An assumption of the energy present in C2H5 internal
modes, along with the measurement of the HCl internal state
and the known energetics of the system, determines the en-
ergy available for kinetic release into products and thus the
magnitude of the center-of-mass speed uHCl . This assump-
The analysis detailed in Secs. III B and III C has con-
cerned a single product state, HCl ͑ ϭ0, Jϭ1͒, populated by
v
the ClϩC2H6 reaction. These data were presented first and
most comprehensively because HCl product is most likely to
be formed in this state ͑see Fig. 1͒. One of the strengths of
the photoloc technique, however, is its ability to measure
speed distributions with complete product state selectivity.
Figure 9 presents the isotropic core-extracted time profiles
tion fixes the relation between ␤ and , and in Fig. 8͑a͒,
for HCl( ϭ0,J) for Jϭ1, Jϭ3, Jϭ6, and Jϭ8; the corre-
v
v
␤( ) contours for varying degrees of ethyl excitation have
sponding state-resolved differential cross sections resulting
from analysis, again assuming no C2H5 excitation, are shown
alongside each profile. The speed distributions from which
these cross sections were derived were verified as nascent by
ascertaining that the profiles did not change between very
short photolysis/probe time delays and the delays used to
acquire the data shown. The Jϭ1 and Jϭ3 profiles are simi-
lar, and this similarity is reflected in nearly identical differ-
ential cross sections for these states. A marked change in the
v
been placed over the experimental data. The anisotropy data
overlaps the outermost contours, indicating that very little
energy from the reaction appears in the internal modes of the
C2H5 radical. Alternately, by inverting Eq. ͑4͒ and applying
Eqs. ͑2͒ and ͑3͒, we can convert the measured anisotropy
into an average C2H5 internal energy. Essentially, this proce-
dure results in a change in coordinates that transforms Figs.
8͑a͒ to 8͑b͒, a plot of ethyl energy as a function of HCl
J. Chem. Phys., Vol. 105, No. 17, 1 November 1996
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7556
Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
formed with little rotational excitation and scatters nearly
isotropically in the center-of-mass frame, with a trend toward
increased back-scattering with increasing HCl rotation.
A possible interpretation of the HCl ͑ ϭ0, Jϭ1͒ differ-
v
ential cross section would attribute the broad scattering, with
a slight peak at side-scattering and somewhat symmetric
drop in the forward and backward direction, to a complex-
forming mechanism that dissociates to products parallel to
the rotational axis of the complex.32 This interpretation is
unsatisfying. The ClϩCH4 and ClϩC2H6 systems are similar
in many ways, and the differences do not seem so severe as
to warrant an abrupt and complete changeover from direct to
complex dynamics. More importantly, complex mechanisms
usually involve considerable randomization of energy into
internal modes of the products. The extremely cold HCl ro-
tational distribution, which takes only 2% of the available
energy into rotation; and the low degree of C2H5 internal
excitation, which takes 7%, indicate direct dynamics for this
reaction.
FIG. 10. Rotational state distribution for the DCl ( ϭ0,J) product from the
v
reaction ClϩC2D6→DClϩC2D5 . Error bars represent 1␴ statistical devia-
tions of replicate measurements. A slight propensity for higher rotational
states is seen, as compared with the nondeuterated reaction.
Additional insight into the dynamics of the ClϩC2H6
system can be obtained from the speed-dependent anisot-
ropy, analysis of which yields the average C2H5 internal ex-
citation. The result, that the reaction deposits little internal
energy into the ethyl radical product, not only allows for
inversion of speed to scattering but furthermore suggests that
the ethyl radical has little effect on the dynamics of the re-
action. This conclusion is further supported by close similari-
ties between the reactions of chlorine atoms with C2H6 and
C2D6 as the dynamical effect by the ethyl radical would be
expected to change with complete deuteration. Characteriza-
tion of the reaction as an atom/pseudo-diatom system, Cl
ϩRH͑D͒, in which the alkyl acts as a spectator, seems to be
borne out by these data. The ability to make this simplifica-
tion is of key interest for attempts to model this and larger
reaction systems.
One model of chemical reactivity holds that product ro-
tational excitation results from an impulsive release of en-
ergy into products from a bent transition state. Under this
model, a linear transition state, where transition state angles
are restricted to small deviations, results in little product ro-
tation; furthermore, linear transition states are assumed to
produce a preference for product back-scattering. This three-
way correspondence between a cold rotational distribution, a
linear transition state, and backward scattering was devel-
oped for and has been applied to a wide number of atom/
diatom systems. For atom/polyatom systems, such as
ClϩC2H6, transition-state forces can be more complex, and
application of an impulsive release model requires further
assumptions. A simple treatment is to model the polyatomic
molecule as a pseudo-diatomic, for example ClϩHϪC2H5.
Thus, by assuming that energy is released along the C–H
bond, the linearity of the Cl–H–C bond can be related to the
final product rotational distribution.
shape of the core-extracted profiles occurs, however, for the
higher rotational states, which upon analysis corresponds to a
shift toward increased back-scattering.
E. Reaction with C2D6
Similar measurements to those described in the preced-
ing sections on the ClϩC2H6 reaction were performed for the
fully deuterated isotopomer. Significant changes in zero-
point energy make this reaction nearly thermoneutral, ⌬Eϭ
Ϫ0.3 kcal/mol.31 The DCl ͑ ϭ0͒ rotational state distribution
v
is shown in Fig. 10. Owing to the decreased exothermicity of
the deuterated reaction, DCl͑ ϭ1͒ formation is once again at
v
the energetic threshold, and although it is observed, the same
problems are present as with HCl͑ ϭ1͒ product from
v
ClϩC2H6. The state distribution was recorded on the R and
S branches of the F͑0,0͒ band of DCl and converted to popu-
lations using correction factors determined experimentally
from spectra of thermal DCl samples. DCl is formed in
higher rotational states than HCl for the analogous reaction.
However, the average rotational energy of the DCl product,
51Ϯ4 cmϪ1, is similar to the value for HCl, 48Ϯ3 cmϪ1. The
analogous result of higher rotational states but equal rota-
tional energies was observed for the ClϩCH4 and ClϩCD4
systems.24 The scattering of the DCl product from ClϩC2D6
is very similar to that of HCl from ClϩC2H6. Once again,
the spatial anisotropy indicates that very little excitation ap-
pears in the C2D5 fragment. The trend of increased back-
scattering with higher rotational states is also observed for
the reaction with perdeuterated ethane.
IV. DISCUSSION
The reaction of atomic chlorine with ethane has been
studied using a photoinitiated scheme that allows the mea-
surement of nascent state distributions and state-resolved dif-
ferential cross sections for the HCl product, as well as the
average internal energy of the C2H5 product associated with
State distributions for several Clϩhydrocarbon reactions
have been published. Distributions from methane, propane,
and isobutane were reported by Varley and Dagdigian;33 pro-
pane was reported by Koplitz and co-workers;34 and perdeu-
terated cyclohexane by Flynn and co-workers.35 In all cases,
each measured product state. The HCl͑ ϭ0͒ product is
v
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Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
7557
rotational excitation of the product was extremely low.
Based on an impulsive release model and analogy to
ClϩCH4, for which a linear transition state is calculated,35,36
these rotational state distributions were used to predict tran-
sition states for Clϩhydrocarbon reactions and to explain
measured product back-scattering for ClϩC4H10.33 This pre-
diction is verified for ClϩCD4, for which members of our
laboratory measured a cold rotational distribution and com-
plete back-scattering for the DCl product.24 In light of these
data, the cold rotational distribution and broad, nearly isotro-
pic scattering evidenced by ClϩC2H6 seem surprising,
though they are similar to recent state and scattering mea-
surements on Clϩisobutane.37 We present an alternate model
for ClϩC2H6 reactivity that explains how isotropic scattering
is consistent with low HCl rotational excitation; furthermore,
the model presented is a direct extension of the model used
to explain ClϩCD4 dynamics.
reaction. This simple model results in a relation between
reaction probability and impact parameter
b2
d2
ET 1Ϫ
уE ,
͑5͒
ͩ
ͪ
0
where ET is the reagent translational energy, E0 is the barrier
energy, and b is the impact parameter, normalized by a dis-
tance d at which reaction occurs. This equation can then be
more broadly applied to yield a differential cross section,
based on the hard-sphere relation between impact parameter
and scattering angle, to produce the following equations;24
1
p␲d2, Ϫ1рcos ␪Ͻcos ␪
d␴
max
2
ϭ
͑6͒
ͭ
d cos ␪
0, cos ␪maxϽcos ␪р1
and
2E0
cos ␪maxϭ1Ϫ
.
͑7͒
ET
These equations qualitatively describe the back-scattering
observed for the ClϩCD4 system, where cos ␪maxϭϪ0.83.
The larger collision energy and smaller barrier for ClϩC2H6
in this experiment yield cos ␪maxϭ0.93, essentially in agree-
ment with the nearly isotropic scattering seen for the system.
A modified version of the line-of-centers model that includes
a barrier dependence on C–H–Cl transition state angle, as
presented by Smith,39 would predict a decrease in scattering
intensity in the forward direction, in contrast to the step-
function differential cross section described in Eq. ͑6͒. This
prediction would model the experimentally observed scatter-
ing more accurately; however, quantitative comparison to
this model requires knowledge concerning the C–H–Cl
transition-state bending potential. Note that the simple line-
of-centers model makes testable predictions concerning
ClϩC2H6 scattering as a function of collision energy. The
scattering is predicted to remain unchanged at higher colli-
sion energies, whereas lower collision energies are predicted
to produce more side- and back-scattered distributions that,
when the energy is comparable to the ClϩC2H6 barrier, will
eventually mirror the complete back-scattering seen in the
ClϩCD4 reaction. Because of the low activation barrier and
the relatively high collision energy for the ClϩC2H6 reac-
tion, the role of the ethane molecule is essentially that of a
‘‘ball of hydrogens’’; regardless of where the chlorine im-
pacts the ethane, a hydrogen atom can be successfully ab-
stracted.
A. Line-of-centers model
Further insight into how a reaction scatters isotropically
with little rotational excitation is gained through analogy to
the correlated state and scattering measurements of the vibra-
tionally excited reaction ClϩCH ͑ 3ϭ1͒.13 The HCl ͑ ϭ1͒
v
v
4
product from this reaction is no more rotationally excited
than HCl͑ ϭ0͒ from ClϩCH ͑ ϭ0͒. In contrast to the
v
v
4
backward-scattering seen for the products from ground-state
methane, the vibrationally excited products scatter with a
distribution peaked sharply in the forward direction. These
products were posited to result from a nonimpulsive strip-
ping mechanism that originated from collisions at large im-
pact parameters that provided little or no torque to the de-
parting molecule. This system was proposed to show such a
radical difference in behavior as a consequence of the vibra-
tional excitation of the reagent. The physical model pre-
sented suggested that the vibrational excitation removed or
significantly lowered the barrier to reaction; a later quasiclas-
sical trajectory study of this reactive system required a slight
well in the potential surface to reproduce the experimental
results.38 In a similar fashion, a small reactive barrier for the
ClϩC2H6 reaction could allow analogous nonimpulsive
stripping for a vibrationally unexcited reaction, resulting in
forward-scattered product and low rotational excitation. The
barrier to the reaction is not known, but analysis of kinetic
data yields an activation energy of 70 cmϪ1 at 220–600 K,
which is 4% of the 1900 cmϪ1 collision energy available to
the system. We propose that this large excess of collision
energy is what accounts for the striking differences in scat-
tering between the ClϩC2H6 and ClϩCD4 systems; the bar-
B. HCl rotation and the Cl-H-C2H5 transition state
The transition state for the ClϩCH4 reaction has been
predicted to be linear based on ab initio calculations,35,36 and
a narrowly constrained geometry is indicated by the small
preexponential factor in the thermal rate expression.1 A simi-
lar calculation shows the ClϩC2H6 transition state to be
linear.40 A first assessment might predict this geometry to be
tightly constrained based on the chemical similarities be-
tween CH4 and C2H6. However, the preexponential factor is
eight times greater for the ClϩC2H6 reaction,1 which pre-
rier height for the latter reaction is estimated at 1370 cmϪ1
,
which is 90% of the 1495 cmϪ1 collision energy.
The behavior of the ClϩCD4 system was explained
through the use of the line-of-centers model.32 This model
states that for an activated reaction, any given collision pro-
ceeds toward products if and only if the reactive barrier is
exceeded by the collision energy along the line of centers of
the reagents; motion transverse to this line does not affect the
J. Chem. Phys., Vol. 105, No. 17, 1 November 1996
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7558
Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
dicts looser steric requirements at the transition state. Under
the nonthermal conditions of this experiment, the ClϩC2H6
reaction produces hundreds of times more HCl product than
was seen in previous studies of the ClϩCH4 reaction. Al-
though this ratio cannot be made quantitative because of dif-
ferences in the nozzle expansion, we conclude that ethane is
far more reactive than methane, beyond the extent explain-
able by the differences in product scattering between the two
systems. For any scattering angle, and for any HCl product
state, the interaction of chlorine atoms with C2H6 is more
likely to proceed toward reaction than for CH4. We draw the
conclusion, based on thermal rate data and the observed
magnitude of our signals, that a larger proportion of the
ClϩC2H6 potential energy surface is reactive—that is, the
reaction proceeds through a ‘‘loose’’ transition state.
While a loose transition state and broad, near-isotropic
scattering are in accordance with a large thermal rate for the
ClϩC2H6 reaction, these must be reconciled with the ex-
tremely cold measured product rotational distribution.
Simple models of reactivity describe the rotational excitation
of the product as the result of an impulsive ‘‘push’’ at the
transition state. These models suggest that a cold rotational
distribution indicates that the C–H–Cl bond is always linear
at the transition state, resulting in little or no torque concomi-
tant with product formation. This strict geometrical con-
straint is at odds with the observed reaction rate. A similar
discrepancy was discussed for the ClϩC6D12 ͑deuterated cy-
clohexane͒ reaction by Flynn and co-workers,41 who also
measured cold DCl product rotational temperatures. For that
system, it was suggested that low-frequency modes of the
hydrocarbon reactant could allow a large thermal rate and a
linear transition state. Under this model, the zero-point mo-
tion associated with C–D bending modes was posited to be
sufficient to bring the reactants into a linear configuration for
a large percentage of collisions. This model could be applied
to ClϩC2H6 but does not explain in a fully satisfactory fash-
ion why similar C–H motions in the ClϩCH4 reaction result
in a far smaller thermal rate.
We submit an alternate explanation wherein products are
formed without impulsive release. The connection between
transition-state bend angle and product rotation results from
a model involving sudden forces at the transition state. This
connection is complicated by forces of longer duration or of
longer range than are normally considered in the domain of
the reaction transition state. Therefore, any reactive mecha-
nism that does not require a sudden force on the departing
hydrogen atom allows low rotational excitation to result
from a wide range of geometries.
Forward- and side-scattered products from ClϩC2H6 are
assumed to result from near-miss and glancing impacts of the
atomic chlorine on the ethane. Because very little of the
translational energy is coupled into the reaction coordinate
for these trajectories and because these trajectories require
only small deviations in the direction the chlorine atom trav-
els as it abstracts hydrogen, the interaction necessary with
the ethane potential is weak. This weak interaction allows
hydrogen transfer to occur nonimpulsively in a manner simi-
lar to the stripping mechanism seen for ClϩCH4 ͑␯3ϭ1͒;13
consequently, the rotational distribution is cold. Note that
this model attributes the cold rotational distribution of these
products solely to the kinematics of the reactive collision and
requires no assumptions of the transition-state geometry.
Trajectories that result in back-scattered products require
stronger interactions, as the chlorine atom must abstract hy-
drogen from the ethane and then recoil from the ethyl radi-
cal. These products might be expected to be formed more
impulsively. Back-scattered products are indeed correlated
with higher rotational states, as can be seen from the rota-
tional dependence of the differential cross section presented
in Sec. III D. Even the back-scattered products, however, are
not rotationally excited significantly compared with the total
energy available to products. By assuming these products are
formed impulsively, we can predict a strongly linear transi-
tion state geometry; however, a nonimpulsive mechanism
and a geometrically unconstrained transition state are more
in accordance with the observed reaction rate.
The chemical similarity of the ClϩCH4͑CD4͒ and
ClϩC2H6 reactions is reflected in that both abstractions pro-
ceed via direct dynamics, and both are explained qualita-
tively by a simple line-of-centers model, indicating that re-
agent translational energy along the reactive Cl–H–C axis is
effective in surmounting an energetic barrier to abstraction.
Differences in product scattering are explained under this
model as the direct result of a lower energetic barrier for the
ClϩC2H6 reaction. We propose that the similarity in product
rotational state distributions does not indicate similar geo-
metric constraints for the two reactions, and we rely instead
on thermal reaction rate measurements to predict a loose,
geometrically unconstrained transition state for ClϩC2H6.
This loose transition state is reconciled with the observed
cold rotational distribution by the proposal of a reaction
mechanism that does not involve significant impulsive re-
lease of energy into products. A further experimental verifi-
cation of the differences between the ClϩCH4 and ClϩC2H6
transition states is available in the study of the effect of re-
agent vibrational excitation on reactivity. Previous studies of
ClϩCH4 ͑␯3ϭ1͒ have shown that the effect of vibrational
excitation is to both lower the energetic barrier and to loosen
geometrical constraints to reaction.13,24 A similar study of the
reaction of chlorine with vibrationally excited ethane is the
topic of a forthcoming publication.
The preceding arguments show that no straightforward
relationship necessarily holds between the reaction
transition-state geometry and the measured rotational state
distribution. The results presented in this paper also demon-
strate that no simple correspondence exists between state and
scattering distributions. We emphasize that both product
state distributions and scattering information are necessary to
determine the broader dynamics of the studied system.
ACKNOWLEDGMENT
S.A.K. thanks the National Science Foundation for a
predoctoral fellowship. This work has been supported by the
National Science Foundation under grant No. CHE-93-
22690.
J. Chem. Phys., Vol. 105, No. 17, 1 November 1996
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Kandel et al.: ClϩC2H6→HClϩC2H5 reaction
7559
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